geom3d[StereographicProjection] - find the stereographic projection of a point

Calling Sequence

StereographicProjection(P, P1, s)

Parameters

P

-

the name of the point to be created

P1

-

a point

s

-

a sphere

Description

•

Let S and N be the south pole and the north pole of the sphere s, respectively. If P1 is a point on s, then the computed point P is the stereographic projection of P1 on s to the tangent plane sp at S, i.e., P is the intersection of the line l, which passes through N and P, and sp. If P1 is a point on the tangent plane sp, then the computed point P is a point on the sphere s such that P1 is the stereographic projection of P on s to the tangent plane sp.

•

For a detailed description of the object created P, use the routine detail (i.e., detail(P))

•

The command with(geom3d,StereographicProjection) allows the use of the abbreviated form of this command.

Examples

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Define the point P(4/3,4/3,4/3) on the sphere s with center at (0,0,2) and radius 2